A physically transparent way to find such transport coefficients is the requirement of positive entropy current in the presence of anomalous sources, in accordance with the second law of thermodynamics [1]}. On the other hand, resting on the analogy with gravity, the appearance of the static, equilibrium anomaly transport coefficients can be organized as an order-by-order derivative expansion of the hydrodynamic conservation laws on non-trivial geometric backgrounds with sources [2]}, [3]}, [4]}, [5]}. The gravitational (i.e. thermal [6]}, [7]}) CVE anomaly current at linear order in response has been related to the gravitational anomalies [8]}, [9]}, [5]} that, at least naively, appear only at higher-orders in the hydrodynamic gradient expansion. The precise way how higher-order anomalies can contribute to the transport has lead to many useful insights about relativistic and non-relativistic hydrodynamics, e.g. [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}.
